Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 655, 827, 341 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 655, 827, 341 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 655, 827, 341 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 655, 827, 341 is 1.
HCF(655, 827, 341) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 655, 827, 341 is 1.
Step 1: Since 827 > 655, we apply the division lemma to 827 and 655, to get
827 = 655 x 1 + 172
Step 2: Since the reminder 655 ≠ 0, we apply division lemma to 172 and 655, to get
655 = 172 x 3 + 139
Step 3: We consider the new divisor 172 and the new remainder 139, and apply the division lemma to get
172 = 139 x 1 + 33
We consider the new divisor 139 and the new remainder 33,and apply the division lemma to get
139 = 33 x 4 + 7
We consider the new divisor 33 and the new remainder 7,and apply the division lemma to get
33 = 7 x 4 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 655 and 827 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(33,7) = HCF(139,33) = HCF(172,139) = HCF(655,172) = HCF(827,655) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 341 > 1, we apply the division lemma to 341 and 1, to get
341 = 1 x 341 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 341 is 1
Notice that 1 = HCF(341,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 655, 827, 341?
Answer: HCF of 655, 827, 341 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 655, 827, 341 using Euclid's Algorithm?
Answer: For arbitrary numbers 655, 827, 341 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.